They didn't. But they did measure electron hydrogen in a different way, and got a similar result to the radius with muonic hydrogen.

That makes the other measurement the odd man out. There could still be something unexpected going on with the proton radius in the presence of muons vs electrons, but it's more likely that the larger measurement is simply incorrect for some unknown reason. That discrepancy could still reveal new physics, but it's more likely an unrealized problem with the apparatus.

We haven't. It is in fact one of alternatives considered. The problem is just that the direction doesn't work well.